What does a deep sun line mean in palmistry?

Short answer: A deep sun line usually means the Apollo or recognition theme is clearly marked. It can suggest visible work, creative satisfaction or recognition, but it does not guarantee fame.

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Read my palm
A close view of the middle of a palm, with the three long creases easy to see

What this means

First confirm the line rises toward the ring finger and Mount of Apollo rather than toward Saturn or Mercury.

A deep line often makes the Apollo theme stronger than a faint or broken line, especially when the Apollo mount is balanced.

Read breaks, crosses, islands, branches, the fate line and both hands before making any strong claim about success or status.